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Non-malleable Codes for Bounded Parallel-Time Tampering

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Advances in Cryptology – CRYPTO 2021 (CRYPTO 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12827))

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Abstract

Non-malleable codes allow one to encode data in such a way that once a codeword is being tampered with, the modified codeword is either an encoding of the original message, or a completely unrelated one. Since the introduction of this notion by Dziembowski, Pietrzak, and Wichs (ICS ’10 and J. ACM ’18), there has been a large body of works realizing such coding schemes secure against various classes of tampering functions. It is well known that there is no efficient non-malleable code secure against all polynomial size tampering functions. Nevertheless, no code which is non-malleable for bounded polynomial size attackers is known and obtaining such a code has been a major open problem.

We present the first construction of a non-malleable code secure against all polynomial size tampering functions that have bounded parallel time. This is an even larger class than all bounded polynomial size functions. In particular, this class includes all functions in non-uniform \(\mathbf {NC}\) (and much more). Our construction is in the plain model (i.e., no trusted setup) and relies on several cryptographic assumptions such as keyless hash functions, time-lock puzzles, as well as other standard assumptions. Additionally, our construction has several appealing properties: the complexity of encoding is independent of the class of tampering functions and we can obtain (sub-)exponentially small error.

D. Dachman-Soled—Supported in part by NSF grants #CNS-1933033, #CNS-1453045 (CAREER), and by financial assistance awards 70NANB15H328 and 70NANB19H126 from the U.S. Department of Commerce, National Institute of Standards and Technology.

R. Pass—Supported in part by NSF Award SATC-1704788, NSF Award RI-1703846, AFOSR Award FA9550-18-1-0267, and a JP Morgan Faculty Award. This material is based upon work supported by DARPA under Agreement No. HR00110C0086 and Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via 2019-19-020700006. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of DARPA, ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.

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Notes

  1. 1.

    Here is the attack: the tampering function can decode the codeword and if it contains some pre-defined message (say all 0 s), then it replaces it with garbage (which might not even correspond to a valid codeword), and otherwise it does not change the input.

  2. 2.

    These are “succinct” one-message arguments for languages in \(\mathbf {P}\), with proof length which is a fixed polynomial, independent of the time it takes to decide the language [28].

  3. 3.

    While keyless multi-collision resistance is a relatively new assumption, it is a natural and simple security property for keyless cryptographic hash functions, which in particular is satisfies by a random function.

  4. 4.

    Non-interactive witness-indistinguishable proofs are known to exist based on various assumptions: trapdoor permutations and a particular derandomization-type assumption [13], cryptographic bilinear maps [48], or indistinguishability obfuscation and one-way permutations [21].

  5. 5.

    Recall that time-lock puzzles are a cryptographic mechanism for sending messages “to the future”, by allowing a sender to quickly generate a puzzle with an underlying message that remains hidden until a receiver spends a moderately large amount of time solving it. Non-malleability guarantees that not only the puzzle hides the underlying message, but actually it is hard to “maul” it into a puzzle with a different “related” message.

  6. 6.

    Actually, Bitansky and Lin [20] formulate an assumption about incompressible functions which is implied by keyless multi-collision resistant hash functions..

  7. 7.

    Actually, Barak and Pass [14] formulate an assumption regarding the existence of a language in \(\mathbf {P}\) which is hard to sample in slightly super-polynomial-time but easy to sample in a slightly larger super-polynomial-time. The existence of a keyless collision resistance hash function with sub-exponential hardness implies such a language.

  8. 8.

    See Footnote 6.

  9. 9.

    This kind of zero-knowledge simulation is known as strong super-polynomial simulation. Recently, Khurana and Sahai [52] managed to obtain it in two rounds, but we need a non-interactive scheme.

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Authors and Affiliations

  1. University of Maryland, College Park, USA

    Dana Dachman-Soled

  2. Hebrew University of Jerusalem and NTT Research, Jerusalem, Israel

    Ilan Komargodski

  3. Cornell Tech, New York City, USA

    Rafael Pass

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  1. Columbia University, New York City, NY, USA

    Tal Malkin

  2. University of Michigan, Ann Arbor, MI, USA

    Chris Peikert

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Dachman-Soled, D., Komargodski, I., Pass, R. (2021). Non-malleable Codes for Bounded Parallel-Time Tampering. In: Malkin, T., Peikert, C. (eds) Advances in Cryptology – CRYPTO 2021. CRYPTO 2021. Lecture Notes in Computer Science(), vol 12827. Springer, Cham. https://doi.org/10.1007/978-3-030-84252-9_18

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